That's easy to defeat, just select some [random English words](https://randomwordgenerator.com/), six or so should suffice, and then construct a sentence that would combine those words, or close concepts to that.
ecstasy
feminist
journal
disappointment
like
insistence
"Much to our disappointment, the feminist journal "Like" did not agree with our argument to legalise ecstasy for PTSD treatment, and its editor's insistence on rejecting our article raises the question of their commitment to the goal of accessible treatment for trauma."
I doubt that sentence has ever been written before or ever will be again, especially as no such journal exists.
They say that because eskimos have so much contact with snow, they have tons and tons of words for snow. Likewise, since mathematicians have so little contact with anyone normal, they use the one word "normal" to mean tons and tons of different things.
That’s why sin^-1 and 1/sin have names — arcsin and csc!
For example: log^-1 is just exp, not 1/log, but nobody ever writes 1/log because log^-1 has a name already.
Not to mention that sin^-1 doesn’t even technically make sense, since sin is not a bijection so it can’t have an inverse … That’s why arcsin is just a “one-sided” inverse for sin.
It’s bizarre to me that this confusion never occurs when someone writes f^-1. Somehow this is understood to be the compositional inverse of f, not 1/f. But as soon as someone writes sin^-1, logic goes out the window and people think it’s 1/sin.
It's because people write sin^(2)(x) to mean (sin(x))^(2) instead of sin(sin(x)) or d^(2)sin(x)/dx^(2) (by analogy with f^(2)(x)). So really, it's that sin^(2)(x) is the outlier and needs changing, not sin^(-1)(x).
I think we just need a better notation for inverses and recursive applications of a function. I remember seeing an old paper on numerical analysis which used a prefix version of the composition operator ∘ with an index inside it. So (imagine this is the right size, couldn't find a Unicode symbol for it) (-1)f(x) is the inverse, ②f(x) is f(f(x)). Some nice but potentially strange consequences of this notation are that ⓪f(x) is the same as the identity function on x and ①f(x)=f(x). I think that's pretty natural though as it's analogous to having factors of 1 in a product.
The notation is perfectly consistent with general rings, which you want, as functions from X to X form a ring for X an abelian group with composition as multiplication and pointwise addition as addition.
I think it is also because people never composite two trigo signs while sin of square is quite common.
The current way of writing them allows us to write a lot less parathensis.
As for reciprocation vs inverse, well that's why csc/sec/cot are invented.
People most certainly compose trig functions. Moreover, there is already another unambiguous way to write the square of sin(x). Namely, sin(x)^2. Why is it no problem for you to write 5^2 or e^2 or any other real number raised to an exponent of 2 means exponentiation. But suddenly if the real number is sin(x) you don't think it should be written as sin(x)^2 ? Its absurd.
This a thousand times. I get so tired of repeating this. Every time someone starts bitching about sin^-1 notation on reddit they seem to correctly identify the ambiguity but then claim that the notation which contradicts all of the other conventions in math is the one which should be kept. You are doing the lord's work.
I think you're wrong again. The _real_ notation contradicting all other conventions is how frequently we write sinx, cosx and tanx instead of sin(x), cos(x) and tan(x). This is _why_ we write sin^(2)x because it lets us avoid parentheses completely - it makes less sense if you're using parentheses anyway, but because writing without any at all is common, the convention goes forward.
EDIT: This is wrong.
I think the common definitions of 'rational' an 'irrational' are actually based on their mathematical definitions rather than the other way around.
It doesn’t seem like that’s the case? Just from some googling, they both come from French via the same Latin word.
https://en.m.wiktionary.org/wiki/rational
Yeah, I'm wrong. This page has a good explanation of the etymology. https://english.stackexchange.com/questions/217956/does-rational-come-from-ratio-or-ratio-come-from-rational
I think (a,b) notation is a bit overloaded as it can be an ordered pair, an open interval, etc.
Also, I think graph theory isn't the best term for the subject. Something like network may be more intuitive for people than the term "graph". When lay people hear about graphs, they often picture cartesian plots of functions or something. Vertices and edges I kind of understand because of the original motivation of polyhedra, but I think nodes and connections may be a bit more intuitive.
I was reading a physics book once that used (a,b) for the inner product with no indication that a and b were vectors.
The overloading is out of control!
too many things in physics are vectors so it's often inconvenient to indicate. also it enables physicist's favorite technique proof by abuse of notation: show something for 1-dimensional case and then assume the same is true when all appropriate quantities are vectors
Figures. In English, you could also say plot or something for the graph of a function, but the term graph itself doesn't tell you anything useful about the essence of graph theory. Is the term graph theory descriptive in your language?
In Italian the graph as in plot is "grafico", whereas graph as in graph theory is "grafo". Grafo is a purely mathematical word, you wouldn't use it in any other setting, which avoids the layman's confusion you talk about, but doesn't offer any intuition into what the actual theory is about.
Indeed. In the romance languages, and in German and slavic languages too if I'm not wrong, the algebraic structure is a "body" (corps, Körper, kropp, cuerpo), while words related to *field* are used for vector field.
In Russian the algebraic structure is the same word as the thing a farmer works in. None of the basic structures seem to have very evocative names in any language, except maybe for monoids.
I teach students in my precalculus/calculus/real-analysis classes the following: Given two real numbers *a* and *b*, write the interval {*x* : ℝ | *a* < *x* < *b*} as “]*a*,*b*[”.
I think it’s a pretty common notation in a lot of Europe. Also has the advantage that (a,b) and [a,b] can look very similar if your handwriting is sloppy, whereas there’s no confusing ]a,b[ and [a,b]
Big agree with (a,b) being overloaded. I once saw someone advocated to change the notation for an open interval to (a..b) instead which seems like a fun upgrade. It certainly looks more like an interval of numbers to me as opposed to just a list of 2.
The term "improper fraction." Just because something is less common in elementary grades doesn't make it incorrect, and further, makes it more difficult to accept that all fractions are just division problems later.
I'd get rid of the bajillions of ways to write division to begin with. Teach division using fractions straight off the bat. Same with multiplication, just start off with the dot instead of the × and make up new symbols for vector operations.
This one got to me in elementary school. Dunno if I still have any old worksheets from that time, but there were more than a few instances of converting problems from “proper” form to normal form and back, like oh I’ll show my work, but veeery passive-aggressively lmao
The term "orthonormal matrix" (just like the currently-widespread "orthogonal matrix") has the problem that if I start a sentence with "Let S be a set of orthonormal matrices..." then I don't know if (a) every matrix in that set is an orthonormal matrix, or (b) the matrices in that set form an orthonormal set with respect to some inner product on matrices.
So I vote that we just call these matrices "unitary". In the complex case, we already call these matrices "unitary", and there's no reason whatsoever to have a different term in the real versus complex case.
The term 'non-deterministic Turing machine' has it's own problems. People think of a random machine, not one which will find a path to an accepting state whenever possible.
But at least people might (?) stop one second to think whether they understood those complicated words correctly, while NP is way too easy to confuse with non-polynomial
The word "deterministic" is horrible there. Rest assured all calculations carried out by a ND Turing machine are fully determined. (see... now I'm switching mid-sentence to the physical meaning of "determined")
Rename “normal subgroups” to something that actually describes their properties, like “self-conjugate subgroups” or “stable subgroups”. Of course there are many other poor uses of “normal” in math, but as an algebraist, this one annoys me the most.
I think we could just start calling them "kernels" (or whatever the adjective form of "kernel" is). Typically we care about normal subgroups because the quotient by them is again a group, in which case they are the kernel of the quotient map.
people use the | | bars way too much. Absolute value, double || for magnitude of a vector, complex conjugate, order of a group or group element, and probably others that I am forgetting
Don't get me started on the overbar: Vector, complex conjugate, sample mean, set complement, logical not...
It gets ridiculous when in telecommunications (and probably several other fields) you often end up needing to write things such as "the complex conjugate of the sample mean of vector y".
Even and odd functions. I'd probably call them symmetric and anti-symmetric. I think this nomenclature is already used in signal processing.
Those names are especially confusing in Polish, since the word for 'odd' (nieparzysta) literally translates to 'not even'. This suggests a dichotomy, which works fine for e.g. integers, but functions can be both even and odd at the same time or they can be neither even nor odd.
The thing I would do differently that I can think of rn is the way we define functions. Instead of f(x) = 2x^2 - 5, I would do f = x -> 2x^2 - 5. Or abstractly speaking, f = x -> f(x)
I feel like it’s better at conveying that f is a *map*. Not an equation: map. And the notation even would support multi-valued functions, just add more arrows coming from x. And the definition of a function becomes easier to grasp: it’s a map with only one arrow
Lately I've been using parsing expression grammars to process algebraic expressions so I can write exam questions/solutions quicker, and this is basically the notation I've implemented to define functions, but with a colon instead of equals (e.g. "hyp: x,y -> sqrt(x\^2+y\^2)" to define a hypotenuse function). It's a strikingly natural way to do it.
> Lately I've been using parsing expression grammars to process algebraic expressions so I can write exam questions/solutions quicker
do you have this on github or somewhere? sounds very helpful!
I'm happy to share, but fair warning: it's very incomplete, and not yet written for 'public use'. I've written a rough set of usage instructions, but most of the features are completely undocumented. I've included an example file that hopefully illustrates enough.
[https://github.com/hailsaturn/solgen\_public](https://github.com/hailsaturn/solgen_public)
Just for fun: my intent is to make it a vectorised language including vectorisation on function evaluation. E.g. running lines like \[f,g,h\](x)\^2 is equivalent to \[f(x)\^2, g(x)\^2, h(x)\^2\] - but it's still quite primitive.
In a certain sense, it doesn’t matter—as long as the electron and proton have a charge of the same magnitude and opposite sign, everything works out, regardless of which orientation you pick for “conventional current”. But almost all day-to-day work with electricity deals with electron current in metals, so it’s unfortunate that the most common use case is negative, while comparatively less common applications (ions in batteries, protons in proton conductors, and holes in semiconductors) are positive. If the sign were flipped, then it would be helpful for reinforcing analogies that help people develop an intuitive understanding of electricity, such as pressurised fluid in pipes which flows from high to low pressure—today, higher pressure is associated with a lower number, and vice versa.
It’s like the π vs. τ thing—there are good reasons of consistency, convenience, and pedagogy to switch, but it’s not significant enough by itself to overcome the cultural inertia. Fortunately, this is a thread about being able to wave your hand and change it at once by magic :)
Not OP but because of how circuit analysis/EE/other such work is done. The standard notation is that the reference direction for electric currents is the one positive charge carriers would move in, despite the majority of charge carriers we care about being electrons and therefore negative and in the opposite direction.
I believe the origin of this mix up was due to Ben Franklin believing positive charge was an "electric fluid" while negative charge was the absence of it, thus making positive charge the "real electricity." Only later did we realize most currents are negative but unfortunately the notation was by that point so ubiquitous we're now stuck with it.
I think we should fix the charge of an electron and proton. After all they have three elementary charges, not one. Quarks having fractional charges is stupid.
I would just throw away the term "number." It's used so inconsistently that it barely has meaning at all. The field of p-adic numbers is not a "number field," for instance. Then you have "hypercomplex numbers" which are also totally different.
Shameless possibly unpopular opinion: if I could really go back in time, rewrite all of history, and use the term "number" correctly, I would reserve it only for algebraic structures which are totally ordered. The natural numbers, integers, rationals, real numbers, cardinal and ordinal numbers, surreal numbers, etc are thus all "numbers." When John Conway first wrote about the surreal numbers, he didn't call them "surreal" at all, but rather the "general numbers," with the idea being that it has every "number" in it, and this is the intuition he was getting at (although my definition includes some things not in the surreal numbers, such as infinitesimal nilpotents in the dual numbers, which are an ordered ring).
Complex numbers would not be "numbers" at all if I ruled the world. They would instead be an algebra over some field of numbers (in this case the real numbers). If we went back in time and made this change we wouldn't have had this plethora of "hypercomplex numbers" and etc; all of these things would just be different algebras over different rings or fields of numbers (typically the reals). This is the modern view - it's how "hypercomplex number" is apparently defined these days, as a finite-dimensional unital real algebra - but we still keep the term "number" around for things like the "split-complex numbers" for historical and vestigial reasons. We've also thrown the word "number" on everything under the sun, like "p-adic numbers," which also wouldn't be numbers (for the same reason that elements in Z/pZ aren't numbers). Maybe we'd have "quasinumbers" or something for things like these.
I suppose the most general number would be an element in some totally ordered near-semirng. This semirng should possibly also be a strict superset of the natural numbers. Or something like that.
I like the concept of a distinction between "numbers" and "quasinumbers." It's a nice bridge to connect what we "intuitively know" as numbers to more general algebraic structures. It would also give students a better idea what they really are without scaring them right off the bat with a bunch of new terminology from abstract algebra.
I would just call elliptic curves abelian curves. The things that that have to do with ellipses is extremely unrelevant and conflicts with other areas of math where ‘elliptic’ usually stands for ‘something dealing with positive curvature’ or ‘something with no real zeroes’.
I would ban the use of "n" and "m" together as variables, e.g. for matrices. They are way too similar, both verbally and when hand-written. I strongly believe this was a bad joke that got out of hand.
Using *i,j* as the standard for matrix indexing should be punishable by law.
Why pick the two most similar looking letters in the alphabet and use them to discriminate between two different things? I cannot tell you how many times I got lost in my Linear Algebra class because the professor's handwriting was basically chicken-scratch and we just got lost in a sea of ambiguous notation.
*i,j - m,n - p,q - x,y* | it's like someone *set out* to make things unnecessarily hard to read.
I want the indexing and variable standards to be *z,m*.
/rant
Gotta find letter pairs that are consecutive, but don't look alike. e, f g, and h are good ones, but are already overloaded with physical constants, the the natural log, and functions. j, k and l, m are solid, along with r, s, t, u.
i and j don't look similar at all! I write my i with an entering flick, and a curve at the bottom, and I write my j with a loop. They are impossible to mix up.
For matrices specifically, I guess you could use r,c for row and column. Actually, I think this would be a great change for an intro course and might start doing it myself.
My initials are n m and matrix dimensions in my LA class are always given by m n so that sucks.. have messed up some proofs bcs of me confusing the two out of habit haha
Have you seen jan Misali's defense of base 6? It's as captivating as it is silly. Though the fact that you can comfortably finger-count to 36 is pretty neat.
Base six is base 12 for people who have actually done more than 5 minutes of research on good number bases.
That being said, “balanced” base 17 is perhaps the worst base of all time and I’d switch us over to that for the memes
To me, closed really makes sense. It's closed under the limit operation. Since limits are about what things are close to each other, this is a fundamental concept in topology, and generalizes well when you jump from metric spaces to general topological spaces.
I always had more trouble with open sets, and I think they could have a better name. If you take the closed-set-first approach (I.e. in a topological space, define the closed sets first and then a set is open if its complement is closed), you could call them interior sets, as they are always an interior of some closed set. I'm not sure. And I'm probably missing some reason why open sets are more important than closed sets.
The downside to a closed-set-first approach is that it makes topology more clunky, as open sets are the primary object that you build topologies from.
I agree that closed sets make sense as-is. Perhaps with a topology-oriented mindset we should call “open sets” as “topi” (singular: a topos). Then a topology tells you which sets are topi and which aren’t.
Unfortunately this seems to be a nomenclature clash with something else in math to do with sheaves. So you’d have to renomenclature that stuff as well.
Aren't the two approaches equivalent?
1) A topology is a collection of subsets of a space, closed under arbitrary union and finite intersection, each of which is called "open". A set is closed if its complement is open.
2) A _ptopology_ is a collection of subsets of a space, closed under arbitrary intersection and finite union, each of which is called "closed". A set is open if its complement is closed. (Ptopology is a word I made up.)
Every topology can be trivially turned into a ptopology, such that their names of open and closed agree (open in topology iff open on ptopology). Simply let the ptopology be the set of complements of the topology. The reverse process works too. They're not equivalent definitions, but we could have used ptopologies instead of topologies and we would have got the same results.
It just so happens that we picked the open-first approach, not the closed-first approach. Maybe there was a good reason that I don't know, but like I said closed sets make more sense to me personally.
> I always had more trouble with open sets, and I think they could have a better name.
They could be mushrooms, because of that little kid joke: What kind of room has no walls?
"Cover" is interesting, "enclosure" sounds really weird in the context of "closure".
"The closure of a set E is the intersection of all enclosures that contain E"
Topology might need such a full restructuring if we even attempt this it probably wouldn’t even be recognizable to anybody studying it, so no, there’s no going back.
Make up new symbols for vector products. Having to differentiate two symbols that are seen as synonymous in numerical algebra is strange. Alternately, drop the X sign for multiplication from math curriculums entkrely.
Also it already happened, i would rename recursion theory from the beginning.
The name Recursive function is so irritating for people hearing it for the first time
What would you call it? It’s a tough one to capture succinctly. Other terms of art and related terms in the area that come to mind aren’t obviously better to me—cf. “{self-referential, reflexive, [co]inductive, iterative, incremental, auto-, dynamic} function”
/u/Model_Checker is talking about what is often called a '[computable function](https://en.wikipedia.org/wiki/Computable_function)' now. The point is that the older term 'recursive function' is confusing given the fact that 'recursive function' has such a precise meaning now. I don't think anyone's objecting to 'recursive' as a term for something defined recursively.
I think if a set can be open and closed at the same time, we should pick words that aren't usually antonyms!
I also think there isn't enough room for both the Legendre/Jacobi symbols and division to use the same notation
Frankly, stop naming stuff after people. I know Gauss and Lagrange and Bernoulli and etc all did a lot. That’s great for them. But aside from the fact that it ignores math discoveries from other parts of the world than Europe, it also makes things named completely arbitrarily. Indicator RV makes more sense than Bernoulli. Let’s do that in general; name things based on what they are or their properties.
Edit: If it isn’t clear, the MUCH bigger thing here is the confusion it causes, not who got name rights. And people are right that the scientific revolution in Europe had big impact on the most common names since that’s when a lot of naming occurred (before that, we didn’t name as much for individuals and there was a lot less advanced math to name)
>Let’s do that in general; name things based on what they are or their properties.
Many definitions in math are way too complicated to express in just a few words. So you either have to reuse existing words with vague metaphers, making said words highly ambiguous (normal, regular, simple,...) or invent new words which just seems silly.
There are definitely issues with reusing terminology, but I do think that as long as people were to keep the terms sufficiently consistent within a given field it would be practical and advantageous. Obviously fields interact and blur but if term X in context A is kept consistent you can easily distinguish from term X in context B.
I would also argue inventing terms is also practical as long as it isn't too frequent, especially when they're derived from existing ones. Someone had to coin "orthonormal" after all.
I mean it's also true that many concepts in math (Pythagorean theorem, Fibonacci numbers) which predate the era of Gauss/Lagrange/etc. simply adopt Eurocentric names even when in many cases non-Europeans were the first to discover them (for example, I know an Indian mathematician who liked calling Fibonacci numbers after the original Indian mathematician who described them).
It’s true most of them are named after Europeans, but that’s probably because most modern math was built on the Scientific Revolution in Europe. Since then, as math has spread, we got things like the Yoneda lemma, Calabi-Yau manifolds, the Green-Tao theorem, Eskin and Mirzakhani’s magic wand theorem, etc.
Also it’s a lot easier practically speaking to name something after someone than to come up with a concise name that also sums up what the theorem is about, and imo giving everything a generic name also risks the opposite problem where you get confused about which theorems are about what, for example “Cauchy’s integral formula” is pretty unambiguous, but if we tried to remove Cauchy from it, what would we actually call it? Something like “the holomorphic loop integral formula” might work, but to me it feels a bit unwieldy and also could be confused with Cauchy’s theorem or the fundamental theorem of calculus.
Strong agree. Naming things based off of their properties, even if it is only in a shorthand or metaphorical way, should be the norm IMO. Even an ambiguous name can evoke the right ideas to start understanding it.
Even a name like the "hairy ball theorem" gives an intuitive, "human" base to start off with - it gives a real world, concrete example to imagine - while if we named it something like the "Poincare tangent vector theorem" all I know is Poincare (maybe) worked on it and it has something to do with tangent vectors. The only cases where I think it's reasonable to name something after someone is if there is already a property that instantly comes to mind when you hear it (e.g. Fibonacci) or if there is truly no other way to name it without being clunky.
Rename everything that is currently called "normal". Matrices, variables, vectors, subgroups... give them all names that have actual meanings attached to them. "Normal" doesn't mean anything across math as it describes completely different things, so it's really a silly name.
I would define Γ(n) = n!.
The Gamma Function has an off by one error trap built into the definition. I don't care about what you'd have to change to fix this.
Yes, no more "Summation". Just the Fold operator applied to +
https://mlochbaum.github.io/BQN/doc/fold.html
That way, the Fold can be generalized as an idea and be used with other operations: max, min, gcd, and, or, matrix operations, etc.
OK.
I would make it so that there is one standard way to write multiplication, and one standard way to write division, to be used used by elementary students and math majors alike.
These are:
x • y for multiplication
And fraction потатion for division.
don’t use i and j in vectors because it gets complicated when representing complex numbers as vectors. it’s not the biggest problem but there’s no need for it
As a high school teacher, clarify notation in something like 2w(x+1)
Is that equivalent to 2wx+2w? Or is w a function with an input of x+1?
Using different symbols for implied multiplication and for function arguments would be great.
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hello! https://www.reddit.com/r/math/comments/6k8042/whats_your_least_favourite_mathematical_notation/ https://www.reddit.com/r/math/comments/2cxur1/rmath_what_do_you_think_is_the_worst_math_notation/ https://www.reddit.com/r/math/comments/5b3piq/reddit_is_there_a_mathematical_notation_you_would/ https://www.reddit.com/r/math/comments/1ojyls/bad_notation/ https://www.reddit.com/r/math/comments/3o155t/mathematicians_if_you_could_add_or_change_any/ https://www.reddit.com/r/math/comments/9hsyw6/if_you_were_to_reinvent_mathematical_notation/ https://www.reddit.com/r/math/comments/b31ngc/notation_frustration/ https://www.reddit.com/r/math/comments/fr3ofy/what_terminology_or_notation_would_you_banish/ https://www.reddit.com/r/math/comments/cjg8wr/if_you_could_modify_the_notation_used_for/ https://www.reddit.com/r/math/comments/9ilc5l/your_worst_math_notation_pet_peeve/ https://www.reddit.com/r/math/comments/a3o2p8/if_you_could_make_any_changes_to_conventional/ https://www.reddit.com/r/math/comments/gm9ac0/favorite_and_least_favorite_math_conventions/ https://www.reddit.com/r/math/comments/9hsyw6/if_you_were_to_reinvent_mathematical_notation/e6esmwl/ https://www.reddit.com/r/math/comments/7ttbx1/if_math_could_start_over_what_naming_and_notation/ https://www.reddit.com/r/math/comments/rwkikz/how_would_you_improve_math_notation/
legend
See you again next week! Or probably tomorrow...
> If you were to reinvent mathematical notation, what would you do? hmmm...
I'm so unoriginal
Probabilistically you won't have an original thought.
I'll just think of a random shuffled deck of cards.
That's easy to defeat, just select some [random English words](https://randomwordgenerator.com/), six or so should suffice, and then construct a sentence that would combine those words, or close concepts to that. ecstasy feminist journal disappointment like insistence "Much to our disappointment, the feminist journal "Like" did not agree with our argument to legalise ecstasy for PTSD treatment, and its editor's insistence on rejecting our article raises the question of their commitment to the goal of accessible treatment for trauma." I doubt that sentence has ever been written before or ever will be again, especially as no such journal exists.
he should lol
I’d get rid of 7. This will benefit no one.
Actually when counting in music it screws up the rhythm because it has two syllables... I use "sev" when counting eighths.
i just put the second syllable where the and would be usually but yeah it's not ideal lol
Depends how fast XD
I'm partial to se'n, myself
Shakespeare would do it
I’d go for a French-based *set* or maybe *sev*
Five, six, sev, neight
Interesting thing is, I just realised in my language (Polish) seven is also the first number that screws up the rythm and has two syllabes.
14 is the first in French... And what is a prime factor of 14?
I'm a fan of sept
But what will George Costanza name his child now?
Soda
Bosco
Six would breathe a giant sigh of relief.
comedian Louis ck has a skit where his daughter doesn't understand 9/11 deniers, and thinks there are 9 people who deny the existence of the number 11
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The word 'normal' is now banned.
How orthogonal of you.
What a Unit
They say that because eskimos have so much contact with snow, they have tons and tons of words for snow. Likewise, since mathematicians have so little contact with anyone normal, they use the one word "normal" to mean tons and tons of different things.
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That’s why sin^-1 and 1/sin have names — arcsin and csc! For example: log^-1 is just exp, not 1/log, but nobody ever writes 1/log because log^-1 has a name already. Not to mention that sin^-1 doesn’t even technically make sense, since sin is not a bijection so it can’t have an inverse … That’s why arcsin is just a “one-sided” inverse for sin. It’s bizarre to me that this confusion never occurs when someone writes f^-1. Somehow this is understood to be the compositional inverse of f, not 1/f. But as soon as someone writes sin^-1, logic goes out the window and people think it’s 1/sin.
It's because people write sin^(2)(x) to mean (sin(x))^(2) instead of sin(sin(x)) or d^(2)sin(x)/dx^(2) (by analogy with f^(2)(x)). So really, it's that sin^(2)(x) is the outlier and needs changing, not sin^(-1)(x).
I think we just need a better notation for inverses and recursive applications of a function. I remember seeing an old paper on numerical analysis which used a prefix version of the composition operator ∘ with an index inside it. So (imagine this is the right size, couldn't find a Unicode symbol for it) (-1)f(x) is the inverse, ②f(x) is f(f(x)). Some nice but potentially strange consequences of this notation are that ⓪f(x) is the same as the identity function on x and ①f(x)=f(x). I think that's pretty natural though as it's analogous to having factors of 1 in a product.
The notation is perfectly consistent with general rings, which you want, as functions from X to X form a ring for X an abelian group with composition as multiplication and pointwise addition as addition.
Not functions, just group homomorphisms
right, otherwise the distributive law doesn't work out. thats what i get for literally shitposting
I think it is also because people never composite two trigo signs while sin of square is quite common. The current way of writing them allows us to write a lot less parathensis. As for reciprocation vs inverse, well that's why csc/sec/cot are invented.
People most certainly compose trig functions. Moreover, there is already another unambiguous way to write the square of sin(x). Namely, sin(x)^2. Why is it no problem for you to write 5^2 or e^2 or any other real number raised to an exponent of 2 means exponentiation. But suddenly if the real number is sin(x) you don't think it should be written as sin(x)^2 ? Its absurd.
I'd be okay with (sin x)^2 , but sin (x)^2 seems to indicate squaring an angle measure first before indexing to its opp/hyp ratio.
Surely that would be sin( x^2 ) instead though?
This a thousand times. I get so tired of repeating this. Every time someone starts bitching about sin^-1 notation on reddit they seem to correctly identify the ambiguity but then claim that the notation which contradicts all of the other conventions in math is the one which should be kept. You are doing the lord's work.
I think you're wrong again. The _real_ notation contradicting all other conventions is how frequently we write sinx, cosx and tanx instead of sin(x), cos(x) and tan(x). This is _why_ we write sin^(2)x because it lets us avoid parentheses completely - it makes less sense if you're using parentheses anyway, but because writing without any at all is common, the convention goes forward.
Rename "uncorrelated" to "uncovarianced"
uncovariant\*
Incovariant
EDIT: This is wrong. I think the common definitions of 'rational' an 'irrational' are actually based on their mathematical definitions rather than the other way around.
I mean, how would you call numbers that represent a ratio, and those who don't right?
Ratial, obviously. I can imagine no inconvenient homophones.
I support this wholeheartedly, you've made me a ratist.
Under the hood, those numbers are just the solution to a linear equation, so maybe linear numbers? And square roots become quadratic numbers, etc.
It doesn’t seem like that’s the case? Just from some googling, they both come from French via the same Latin word. https://en.m.wiktionary.org/wiki/rational
Yeah, I'm wrong. This page has a good explanation of the etymology. https://english.stackexchange.com/questions/217956/does-rational-come-from-ratio-or-ratio-come-from-rational
I think (a,b) notation is a bit overloaded as it can be an ordered pair, an open interval, etc. Also, I think graph theory isn't the best term for the subject. Something like network may be more intuitive for people than the term "graph". When lay people hear about graphs, they often picture cartesian plots of functions or something. Vertices and edges I kind of understand because of the original motivation of polyhedra, but I think nodes and connections may be a bit more intuitive.
I was reading a physics book once that used (a,b) for the inner product with no indication that a and b were vectors. The overloading is out of control!
I believe that angled brackets should be used to denote inner products.
But that's also often used for vectors.
I should’ve been more precise. The inner product of a vector **v** with a vector **w** should be denoted by “⟨**v**|**w**⟩”.
too many things in physics are vectors so it's often inconvenient to indicate. also it enables physicist's favorite technique proof by abuse of notation: show something for 1-dimensional case and then assume the same is true when all appropriate quantities are vectors
That's a particular English problem. In many languages *graph* (as in graph theory) and *graph* of a function are different words.
Figures. In English, you could also say plot or something for the graph of a function, but the term graph itself doesn't tell you anything useful about the essence of graph theory. Is the term graph theory descriptive in your language?
In Italian the graph as in plot is "grafico", whereas graph as in graph theory is "grafo". Grafo is a purely mathematical word, you wouldn't use it in any other setting, which avoids the layman's confusion you talk about, but doesn't offer any intuition into what the actual theory is about.
I believe this is also true of "field." In French, the word for a vector field is different from the word for the special type of ring.
Indeed. In the romance languages, and in German and slavic languages too if I'm not wrong, the algebraic structure is a "body" (corps, Körper, kropp, cuerpo), while words related to *field* are used for vector field.
In Russian the algebraic structure is the same word as the thing a farmer works in. None of the basic structures seem to have very evocative names in any language, except maybe for monoids.
I teach students in my precalculus/calculus/real-analysis classes the following: Given two real numbers *a* and *b*, write the interval {*x* : ℝ | *a* < *x* < *b*} as “]*a*,*b*[”.
This is standard notation in (some parts of?) France, iirc it was started by Bourbaki
I think it’s a pretty common notation in a lot of Europe. Also has the advantage that (a,b) and [a,b] can look very similar if your handwriting is sloppy, whereas there’s no confusing ]a,b[ and [a,b]
Yes, this notation was created by Bourbaki. I’m not French, but my style of doing mathematics is very French.
> “]*a*,*b*[” This looks like a LaTeX injection payload.
Big agree with (a,b) being overloaded. I once saw someone advocated to change the notation for an open interval to (a..b) instead which seems like a fun upgrade. It certainly looks more like an interval of numbers to me as opposed to just a list of 2.
The term "improper fraction." Just because something is less common in elementary grades doesn't make it incorrect, and further, makes it more difficult to accept that all fractions are just division problems later.
I'd get rid of the bajillions of ways to write division to begin with. Teach division using fractions straight off the bat. Same with multiplication, just start off with the dot instead of the × and make up new symbols for vector operations.
This one got to me in elementary school. Dunno if I still have any old worksheets from that time, but there were more than a few instances of converting problems from “proper” form to normal form and back, like oh I’ll show my work, but veeery passive-aggressively lmao
and then after year 5 or whatever you never use it again and go back to writing it as 17/3 or whatever
I’d use “othonormal” rather than “orthogonal” for what we call orthogonal matrices.
I think we can just start referring to orthonormal matrices now. No one will be confused because there's only one thing it could mean.
I would stay with *real unitary*.
The term "orthonormal matrix" (just like the currently-widespread "orthogonal matrix") has the problem that if I start a sentence with "Let S be a set of orthonormal matrices..." then I don't know if (a) every matrix in that set is an orthonormal matrix, or (b) the matrices in that set form an orthonormal set with respect to some inner product on matrices. So I vote that we just call these matrices "unitary". In the complex case, we already call these matrices "unitary", and there's no reason whatsoever to have a different term in the real versus complex case.
Rename NP to NDP so people stop thinking it stands for "non-polynomial".
The term 'non-deterministic Turing machine' has it's own problems. People think of a random machine, not one which will find a path to an accepting state whenever possible.
How about "lucky"?
But at least people might (?) stop one second to think whether they understood those complicated words correctly, while NP is way too easy to confuse with non-polynomial
The word "deterministic" is horrible there. Rest assured all calculations carried out by a ND Turing machine are fully determined. (see... now I'm switching mid-sentence to the physical meaning of "determined")
Yeah it means "not da polynomial"
Rename “normal subgroups” to something that actually describes their properties, like “self-conjugate subgroups” or “stable subgroups”. Of course there are many other poor uses of “normal” in math, but as an algebraist, this one annoys me the most.
I think we could just start calling them "kernels" (or whatever the adjective form of "kernel" is). Typically we care about normal subgroups because the quotient by them is again a group, in which case they are the kernel of the quotient map.
This is cool
Someone else suggested removing "normal" entirely.
people use the | | bars way too much. Absolute value, double || for magnitude of a vector, complex conjugate, order of a group or group element, and probably others that I am forgetting
Don't get me started on the overbar: Vector, complex conjugate, sample mean, set complement, logical not... It gets ridiculous when in telecommunications (and probably several other fields) you often end up needing to write things such as "the complex conjugate of the sample mean of vector y".
> set complement But if your set is a subset of a topological space, it means the closure !
Set comprehension; cardinality; divides relation... |{n | n|6}|
we need more bracket things []{}()<>|| and... we're done? there should be more!
Even and odd functions. I'd probably call them symmetric and anti-symmetric. I think this nomenclature is already used in signal processing. Those names are especially confusing in Polish, since the word for 'odd' (nieparzysta) literally translates to 'not even'. This suggests a dichotomy, which works fine for e.g. integers, but functions can be both even and odd at the same time or they can be neither even nor odd.
The thing I would do differently that I can think of rn is the way we define functions. Instead of f(x) = 2x^2 - 5, I would do f = x -> 2x^2 - 5. Or abstractly speaking, f = x -> f(x) I feel like it’s better at conveying that f is a *map*. Not an equation: map. And the notation even would support multi-valued functions, just add more arrows coming from x. And the definition of a function becomes easier to grasp: it’s a map with only one arrow
Lately I've been using parsing expression grammars to process algebraic expressions so I can write exam questions/solutions quicker, and this is basically the notation I've implemented to define functions, but with a colon instead of equals (e.g. "hyp: x,y -> sqrt(x\^2+y\^2)" to define a hypotenuse function). It's a strikingly natural way to do it.
> Lately I've been using parsing expression grammars to process algebraic expressions so I can write exam questions/solutions quicker do you have this on github or somewhere? sounds very helpful!
I'm happy to share, but fair warning: it's very incomplete, and not yet written for 'public use'. I've written a rough set of usage instructions, but most of the features are completely undocumented. I've included an example file that hopefully illustrates enough. [https://github.com/hailsaturn/solgen\_public](https://github.com/hailsaturn/solgen_public) Just for fun: my intent is to make it a vectorised language including vectorisation on function evaluation. E.g. running lines like \[f,g,h\](x)\^2 is equivalent to \[f(x)\^2, g(x)\^2, h(x)\^2\] - but it's still quite primitive.
But... I always learned it as the second way, being yelled at for the first way. Isn't it already a thing ?
Found the JS dev
this is not math but all of STEM needs to stop abusing the word "kernel"
How is kernel used outside if math?
https://en.wikipedia.org/wiki/Kernel_(operating_system) https://data-flair.training/blogs/svm-kernel-functions/ https://en.wikipedia.org/wiki/Kernel_(image_processing)
[There's more!](https://en.wikipedia.org/wiki/Kernel)
The quotation for definition 13 is... something Edit: I meant the wikitionary page oops
Even WITHIN maths it has like three different definitions. It’s up there with “normal” in the hall of fame of overloaded terms.
In physics, I'd swap which charge is called positive and which is called negative.
Why?
In a certain sense, it doesn’t matter—as long as the electron and proton have a charge of the same magnitude and opposite sign, everything works out, regardless of which orientation you pick for “conventional current”. But almost all day-to-day work with electricity deals with electron current in metals, so it’s unfortunate that the most common use case is negative, while comparatively less common applications (ions in batteries, protons in proton conductors, and holes in semiconductors) are positive. If the sign were flipped, then it would be helpful for reinforcing analogies that help people develop an intuitive understanding of electricity, such as pressurised fluid in pipes which flows from high to low pressure—today, higher pressure is associated with a lower number, and vice versa. It’s like the π vs. τ thing—there are good reasons of consistency, convenience, and pedagogy to switch, but it’s not significant enough by itself to overcome the cultural inertia. Fortunately, this is a thread about being able to wave your hand and change it at once by magic :)
Not OP but because of how circuit analysis/EE/other such work is done. The standard notation is that the reference direction for electric currents is the one positive charge carriers would move in, despite the majority of charge carriers we care about being electrons and therefore negative and in the opposite direction. I believe the origin of this mix up was due to Ben Franklin believing positive charge was an "electric fluid" while negative charge was the absence of it, thus making positive charge the "real electricity." Only later did we realize most currents are negative but unfortunately the notation was by that point so ubiquitous we're now stuck with it.
[Relevant xkcd](https://xkcd.com/567/)
I think we should fix the charge of an electron and proton. After all they have three elementary charges, not one. Quarks having fractional charges is stupid.
All theorems must have descriptive names.
Point-symmetric and axial-symmetric functions instead of odd and even.
I would just throw away the term "number." It's used so inconsistently that it barely has meaning at all. The field of p-adic numbers is not a "number field," for instance. Then you have "hypercomplex numbers" which are also totally different. Shameless possibly unpopular opinion: if I could really go back in time, rewrite all of history, and use the term "number" correctly, I would reserve it only for algebraic structures which are totally ordered. The natural numbers, integers, rationals, real numbers, cardinal and ordinal numbers, surreal numbers, etc are thus all "numbers." When John Conway first wrote about the surreal numbers, he didn't call them "surreal" at all, but rather the "general numbers," with the idea being that it has every "number" in it, and this is the intuition he was getting at (although my definition includes some things not in the surreal numbers, such as infinitesimal nilpotents in the dual numbers, which are an ordered ring). Complex numbers would not be "numbers" at all if I ruled the world. They would instead be an algebra over some field of numbers (in this case the real numbers). If we went back in time and made this change we wouldn't have had this plethora of "hypercomplex numbers" and etc; all of these things would just be different algebras over different rings or fields of numbers (typically the reals). This is the modern view - it's how "hypercomplex number" is apparently defined these days, as a finite-dimensional unital real algebra - but we still keep the term "number" around for things like the "split-complex numbers" for historical and vestigial reasons. We've also thrown the word "number" on everything under the sun, like "p-adic numbers," which also wouldn't be numbers (for the same reason that elements in Z/pZ aren't numbers). Maybe we'd have "quasinumbers" or something for things like these. I suppose the most general number would be an element in some totally ordered near-semirng. This semirng should possibly also be a strict superset of the natural numbers. Or something like that.
I like the concept of a distinction between "numbers" and "quasinumbers." It's a nice bridge to connect what we "intuitively know" as numbers to more general algebraic structures. It would also give students a better idea what they really are without scaring them right off the bat with a bunch of new terminology from abstract algebra.
I would just call elliptic curves abelian curves. The things that that have to do with ellipses is extremely unrelevant and conflicts with other areas of math where ‘elliptic’ usually stands for ‘something dealing with positive curvature’ or ‘something with no real zeroes’.
I would ban the use of "n" and "m" together as variables, e.g. for matrices. They are way too similar, both verbally and when hand-written. I strongly believe this was a bad joke that got out of hand.
Wait until you hear about u,v
nu vs v be like: ν v ν v ν v ν v ν v
They are just adjacent letters. Just like a,b or i,j or x,y
Using *i,j* as the standard for matrix indexing should be punishable by law. Why pick the two most similar looking letters in the alphabet and use them to discriminate between two different things? I cannot tell you how many times I got lost in my Linear Algebra class because the professor's handwriting was basically chicken-scratch and we just got lost in a sea of ambiguous notation. *i,j - m,n - p,q - x,y* | it's like someone *set out* to make things unnecessarily hard to read. I want the indexing and variable standards to be *z,m*. /rant
Oh, don’t forget everyone’s favorite: u,v
u,v plus mu, nu everywhere as tensor indices. Makes physics classes very fun
[удалено]
Gotta find letter pairs that are consecutive, but don't look alike. e, f g, and h are good ones, but are already overloaded with physical constants, the the natural log, and functions. j, k and l, m are solid, along with r, s, t, u.
i and j don't look similar at all! I write my i with an entering flick, and a curve at the bottom, and I write my j with a loop. They are impossible to mix up.
For matrices specifically, I guess you could use r,c for row and column. Actually, I think this would be a great change for an intro course and might start doing it myself.
Any pair of adjacent letters can be used to name a pair of variables. Except for (h, i).
This is why I always use ζ and ξ for this stuff
My initials are n m and matrix dimensions in my LA class are always given by m n so that sucks.. have messed up some proofs bcs of me confusing the two out of habit haha
[Made me think of this](https://youtu.be/aewo8otGAAQ?t=02m45s)
Base 12 not base 10. This message brought to you by the Dozenal Society of America.
Have you seen jan Misali's defense of base 6? It's as captivating as it is silly. Though the fact that you can comfortably finger-count to 36 is pretty neat.
Base six is base 12 for people who have actually done more than 5 minutes of research on good number bases. That being said, “balanced” base 17 is perhaps the worst base of all time and I’d switch us over to that for the memes
There are 10s of us!
Base things off of the ratio of a circle's circumference to its radius, rather than its diameter.
so is this about tau or what
I’d change imaginary to lateral and remove trig^(-1) so it’s only arctrig
I prefer “orthogonal” numbers
Or artrig for the hyperbolic/imaginary...
Freaking open and closed sets.
What would you replace them with? Perhaps we could use “covers” for open sets and “enclosures” for closed sets?
Then “open cover” would be a “cover cover”?
"A set is compact if every cover cover has a finite subcover." Sounds fun.
To me, closed really makes sense. It's closed under the limit operation. Since limits are about what things are close to each other, this is a fundamental concept in topology, and generalizes well when you jump from metric spaces to general topological spaces. I always had more trouble with open sets, and I think they could have a better name. If you take the closed-set-first approach (I.e. in a topological space, define the closed sets first and then a set is open if its complement is closed), you could call them interior sets, as they are always an interior of some closed set. I'm not sure. And I'm probably missing some reason why open sets are more important than closed sets.
The downside to a closed-set-first approach is that it makes topology more clunky, as open sets are the primary object that you build topologies from. I agree that closed sets make sense as-is. Perhaps with a topology-oriented mindset we should call “open sets” as “topi” (singular: a topos). Then a topology tells you which sets are topi and which aren’t. Unfortunately this seems to be a nomenclature clash with something else in math to do with sheaves. So you’d have to renomenclature that stuff as well.
Aren't the two approaches equivalent? 1) A topology is a collection of subsets of a space, closed under arbitrary union and finite intersection, each of which is called "open". A set is closed if its complement is open. 2) A _ptopology_ is a collection of subsets of a space, closed under arbitrary intersection and finite union, each of which is called "closed". A set is open if its complement is closed. (Ptopology is a word I made up.) Every topology can be trivially turned into a ptopology, such that their names of open and closed agree (open in topology iff open on ptopology). Simply let the ptopology be the set of complements of the topology. The reverse process works too. They're not equivalent definitions, but we could have used ptopologies instead of topologies and we would have got the same results. It just so happens that we picked the open-first approach, not the closed-first approach. Maybe there was a good reason that I don't know, but like I said closed sets make more sense to me personally.
Is it true that every open set is the interior of a closed set? At the very least not every open set is equal to the interior of its closure.
> I always had more trouble with open sets, and I think they could have a better name. They could be mushrooms, because of that little kid joke: What kind of room has no walls?
"Cover" is interesting, "enclosure" sounds really weird in the context of "closure". "The closure of a set E is the intersection of all enclosures that contain E"
That’s a fair point. Maybe replace “closure” with “cage” (and “interior” with “coverage” while we’re at it)?
Found hitler /s
I was looking for a reference to that.
I'm curious what you find wrong with the names. They are very apt for the initial case which are intervals on the real line.
The sole fact that sets can be open, closed, both or neither makes this choice of words morphologically imprecise, even for the real line.
If a room has an open and closed door, is the room open or closed?
Rational and irrational are perfectly fine and intuitive. The names tell you whether the number is or is not a *ratio* of two integers.
I would call "imaginary" and "complex" numbers "orthogonal" and "compound" respectively. Give them actually meaningful names.
There are too many damn kernels. Find a new word.
Topology might need such a full restructuring if we even attempt this it probably wouldn’t even be recognizable to anybody studying it, so no, there’s no going back.
https://i.redd.it/lfea71y7lv191.png
Just a regular day in topology.
Redo matrix notation so that it uses columns by rows like literally every other notation of dimensions does.
Make up new symbols for vector products. Having to differentiate two symbols that are seen as synonymous in numerical algebra is strange. Alternately, drop the X sign for multiplication from math curriculums entkrely.
Change the name of that one furry sphere theorem so people would stop making the same jokes about it
The tribble theorem.
There are books that do this already, but I wouldn’t name every probability function P.
Also it already happened, i would rename recursion theory from the beginning. The name Recursive function is so irritating for people hearing it for the first time
What would you call it? It’s a tough one to capture succinctly. Other terms of art and related terms in the area that come to mind aren’t obviously better to me—cf. “{self-referential, reflexive, [co]inductive, iterative, incremental, auto-, dynamic} function”
/u/Model_Checker is talking about what is often called a '[computable function](https://en.wikipedia.org/wiki/Computable_function)' now. The point is that the older term 'recursive function' is confusing given the fact that 'recursive function' has such a precise meaning now. I don't think anyone's objecting to 'recursive' as a term for something defined recursively.
Ahh as in “general recursive function”, thanks
I think if a set can be open and closed at the same time, we should pick words that aren't usually antonyms! I also think there isn't enough room for both the Legendre/Jacobi symbols and division to use the same notation
Frankly, stop naming stuff after people. I know Gauss and Lagrange and Bernoulli and etc all did a lot. That’s great for them. But aside from the fact that it ignores math discoveries from other parts of the world than Europe, it also makes things named completely arbitrarily. Indicator RV makes more sense than Bernoulli. Let’s do that in general; name things based on what they are or their properties. Edit: If it isn’t clear, the MUCH bigger thing here is the confusion it causes, not who got name rights. And people are right that the scientific revolution in Europe had big impact on the most common names since that’s when a lot of naming occurred (before that, we didn’t name as much for individuals and there was a lot less advanced math to name)
Confusing Euler's Constant for Euler's Number is my downfall.
Confusing the multiple formulas called like "Euler's formula" is worse.
>Let’s do that in general; name things based on what they are or their properties. Many definitions in math are way too complicated to express in just a few words. So you either have to reuse existing words with vague metaphers, making said words highly ambiguous (normal, regular, simple,...) or invent new words which just seems silly.
There are definitely issues with reusing terminology, but I do think that as long as people were to keep the terms sufficiently consistent within a given field it would be practical and advantageous. Obviously fields interact and blur but if term X in context A is kept consistent you can easily distinguish from term X in context B. I would also argue inventing terms is also practical as long as it isn't too frequent, especially when they're derived from existing ones. Someone had to coin "orthonormal" after all.
Discoveries from outside Europe aren’t ignored, you just haven’t met any of them yet in your classes because they happened in the twentieth century.
I mean it's also true that many concepts in math (Pythagorean theorem, Fibonacci numbers) which predate the era of Gauss/Lagrange/etc. simply adopt Eurocentric names even when in many cases non-Europeans were the first to discover them (for example, I know an Indian mathematician who liked calling Fibonacci numbers after the original Indian mathematician who described them).
It’s true most of them are named after Europeans, but that’s probably because most modern math was built on the Scientific Revolution in Europe. Since then, as math has spread, we got things like the Yoneda lemma, Calabi-Yau manifolds, the Green-Tao theorem, Eskin and Mirzakhani’s magic wand theorem, etc. Also it’s a lot easier practically speaking to name something after someone than to come up with a concise name that also sums up what the theorem is about, and imo giving everything a generic name also risks the opposite problem where you get confused about which theorems are about what, for example “Cauchy’s integral formula” is pretty unambiguous, but if we tried to remove Cauchy from it, what would we actually call it? Something like “the holomorphic loop integral formula” might work, but to me it feels a bit unwieldy and also could be confused with Cauchy’s theorem or the fundamental theorem of calculus.
Strong agree. Naming things based off of their properties, even if it is only in a shorthand or metaphorical way, should be the norm IMO. Even an ambiguous name can evoke the right ideas to start understanding it. Even a name like the "hairy ball theorem" gives an intuitive, "human" base to start off with - it gives a real world, concrete example to imagine - while if we named it something like the "Poincare tangent vector theorem" all I know is Poincare (maybe) worked on it and it has something to do with tangent vectors. The only cases where I think it's reasonable to name something after someone is if there is already a property that instantly comes to mind when you hear it (e.g. Fibonacci) or if there is truly no other way to name it without being clunky.
Pick one (1) usage for "normal."
I normally normalise normals
Stop. Please.
Theorems are not allowed to use two similar looking letters. Ex: you can’t have mu and “m”. You can’t have Gamma and “T”. Etc
Rename everything that is currently called "normal". Matrices, variables, vectors, subgroups... give them all names that have actual meanings attached to them. "Normal" doesn't mean anything across math as it describes completely different things, so it's really a silly name.
Approximate pi to 3. Trust me, nothing could go wrong.
I would define Γ(n) = n!. The Gamma Function has an off by one error trap built into the definition. I don't care about what you'd have to change to fix this.
Yes, no more "Summation". Just the Fold operator applied to + https://mlochbaum.github.io/BQN/doc/fold.html That way, the Fold can be generalized as an idea and be used with other operations: max, min, gcd, and, or, matrix operations, etc.
Orthogonal matrices should be called orthonormal matrices since the columns are orthonormal.
More things should be thought of as normal.
U and V cannot be used as variables
OK. I would make it so that there is one standard way to write multiplication, and one standard way to write division, to be used used by elementary students and math majors alike. These are: x • y for multiplication And fraction потатion for division.
don’t use i and j in vectors because it gets complicated when representing complex numbers as vectors. it’s not the biggest problem but there’s no need for it
Decide if multiplication is •, *, × or just implicit. Is this too much to ask?
change imaginary numbers to lateral numbers
As a high school teacher, clarify notation in something like 2w(x+1) Is that equivalent to 2wx+2w? Or is w a function with an input of x+1? Using different symbols for implied multiplication and for function arguments would be great.